[jvkersch]

Hence, a very poor approximation to pi is given by 365 × 5⁵ × 4⁴ × 3³ × 2² × 1¹ / 10^10.

[OskarS]

Why would "the number of milliseconds in a year divided by 10 billion" have anything to do with pi?

[Shadow6363]

I feel like I was just nerd sniped, but this drove me crazy until I thought about it for a bit.

If we treat Earth's orbit as a perfect circle, then the number of milliseconds in a year would be its circumference. To get to pi then, we just need to divide that by its diameter or 2*its radius. In addition, we have the circumference in ms so we want to convert that into a distance or the radius into ms so we need the speed the Earth is rotating around the sun.

The average radius of the Earth to the Sun is 149,600,000 km so the diameter is 299,200,000 km. Earth's average orbital speed is 30 km/s or 0.03 km/ms. Combining these two numbers to get ms, (299,200,000 km / 0.03 km/ms) = 9,973,333,333.333 ms, which is very nearly 10 billion.

[efaref]

It's pure coincidence, but "pi seconds is a nanocentury" is a useful mnemonic.

[leetcrew]

no real reason. it's just that 86400000 / 10^2 ~= 0.01 and 365 is relatively close to pi shifted two places.

there's no direct relationship between orbital period and length of day.

[vignesh_m]

3.1536 - thats way to inaccurate to be of any interest imo. Even 22/7 is a way better approximation

[jaclaz]

Though nothing beats Milü in its simplictry and accuracy:

https://en.wikipedia.org/wiki/Milü

355/113: >An easy mnemonic helps memorize this useful fraction by writing down each of the first three odd numbers twice: 1 1 3 3 5 5, then dividing the decimal number represented by the last 3 digits by the decimal number given by the first three digits.

[gpvos]

Why "hence"?